Laplace-Beltrami operator
= Laplace-Beltrami operator
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{title2=$\Delta_g$}
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The Laplace-Beltrami operator is the intrinsic Laplacian determined by a Riemannian metric. In local coordinates it is
$$
\Delta_gf=|g|^{-1/2}\partial_i\left(|g|^{1/2}g^{ij}\partial_jf\right).
$$